一维时齐带反射边界零常返扩散过程回返时的矩

Return time moment of time-homogeneous and null-recurrent one-dimension diffusion with reflection boundary

摘要: 基于半直线 0, \infty ) 带反射边界的一维时齐零常返扩散过程, 探讨了其击中固定点1后首次回返时的矩, 并对回返时Laplace变换所满足的带反射边界条件微分方程的近似解进行了估计；由Tauberian引理获得了回返时概率分布的渐近估计, 并得到了回返时的 \gamma 阶矩有限时, 阶数\gamma 的取值范围．

Abstract: This work aims to study moment of return time of time-homogeneous and null-recurrent one-dimension diffusion on 0,\infty ) with reflection boundary, to solve estimation of approximate solution of differential equation with reflection boundary satisfied by the Laplace transform in return time． Asymptotic estimation of probability distribution in return time is obtained using Tauberian lemma． When \gamma -moment is finite the range of order \gamma is calculated．